Pattern transferable to skin for optical measurements during shaving

ABSTRACT

A removable tattoo for applying a pattern to the skin for use with an optical measurement system to measure forces on the skin such as during shaving. A transfer paper is printed with a random pattern of different size dots. The pattern can have two or three different sized dots. The pattern of dots has a pattern density of between about 40% to about 60%. The pattern is printed with inks suitable for skin contact that are not water soluble so as to withstand a moist shaving environment. The pattern is removable from the test person with alcohol.

FIELD OF THE INVENTION

The present invention relates to a dot pattern transferable to the skinand recognized by an optical measurement technique to detect motion ofthe patterned area in response to an applied force, e.g. shaving.

BACKGROUND OF THE INVENTION

It has been known to use three dimensional (3D) image correlationphotogrammetry as a full-field, non-contact optical inspection techniqueto analyze strain in machine parts and dissected tissue specimens. Thistechnique is described for example in the literature by Tyson, J.,Schmidt, T. Galanulis, K. “Optical Deformation & Strain Measurement inBiomechanics”, in Biophotonics, September 2003, pages 1 to 7; and byTyson, J., Schmidt, T., Galanulis, K., “Biomechanics Deformation andStrain measurements with 3D Image Correlation Photogrammetry”,Experimental Techniques, Vol. 26, No. 5, pages 39-42, September/October2002 (ProQuest Science Journals). This literature describes straintesting of dissected bone, knee tendon, and ligament specimens that havebeen removed from a cadaver and ruptured under tensile testing, of aheart of a vivisectioned frog, and of flexed artificial musclespecimens. Known industrial applications of this measurement system arefor aerospace or machine parts. These biologic specimen and industrialapplications involve objects held in a fixture during testing.Measurement systems of this type are in wide use in the aerospaceindustry and in public universities (including the Universities ofMaine, Wichita State in Kansas, and Akron in Ohio), with at least 300 ofthem in use in Europe and 40 in the United States. For example, theUnited States space agency NASA used this technique to make measurementsof the full Space Shuttle wing leading edge (NASA Johnson Space FlightCenter & Southwest Research) as well as for External Fuel Tank (ET) foamimpacts (Lockheed Martin Manned Space Systems). This technique allowsfor non-contact determination of 3D coordinates and 3D displacements, 3Dspeeds and accelerations, and plane strain tensor and plane strain rate.

An example of a commercially widely available 3D image correlationphotogrammetry digital camera system is the system made by the companyGOM mbh marketed under the trade designation ARAMIS system.

The preparation of the specimen with a pattern is described in the above“Biomechanics Deformation” and “Optical Deformation” articles, oralternatively in the “ARAMIS User Manual”, at pages 26-27, published bythe GOM company (2005), as a high-contrast stochastic (random) patternconsisting of a sprayed-on dye penetrant developer (such as white)overlaid with a sprayed-on black spray (e.g. a matte black spray orgraphite spray), for example by lightly pressing the spray button oncommercially available cans of spray paint. It is also known to applythe pattern by means of a pen or a stencil/spray technique. It is knownthat smooth specimen surfaces are preferred. The pattern can be aregular or random pattern. It is known that it is preferred for thepattern to avoid large areas of constant brightness such as wide lines.It is known that it is preferred to avoid a shiny pattern and to prefera pattern with a matte or dull surface.

Temporary tattoos made from dyes or inks approved for use in food orcosmetics are known for novelty purposes, as body adornment, or to marka person's hand as having paid an admission price. These typicallyinvolve a recognized, ordered arrangement of graphic elements, or text,as known for example in U.S. Pat. Nos. 5,578,353 (Drew, III); 7,011,401(Markey, III); 6,161,554 (Dunlap-Harris); and 6,457,585 (Huffer et al.).Some such tattoos are transferred to the person by the tattoo's having apressure-sensitive adhesive layer. Other such tattoos are printed on apaper substrate with water soluble ink, and the paper placed in contactwith the skin in the presence of moisture and the ink is transferred tothe skin.

Dot patterns are known in eye color-blindness tests such as the Ishiharacolor chart (named after its designer Dr. Shinobu Ishihara, a professorat the University of Tokyo, who published his test in 1917) which usescolored plates having a background of dots in the middle of which is arecognizable regular pattern, differentiated by color, usually in theshape of an Arabic number or English letter, see also U.S. Pat. No.2,937,567 (Hardy) and U.S. Pat. Appln. 2005/0213039 (Ohashi). These eyecharts are usually printed on heavy stock and carefully preservedagainst soiling so as to be used by eye care professionals to diagnosepatients.

There remains a need to determine strain fields on the skin surface of aliving human interacting with a product used on the skin in a mannercomfortable to the test subject person.

There remains a further need to quickly and/or conveniently apply aremovable pattern to a human test subject.

SUMMARY OF THE INVENTION

It is an object of the invention to provide a method of measuring strainon the skin of a living person while the person uses a shaving apparatussuch as a dry shaver or a wet razor to shave hairs on the skin. A wetrazor, also referred to as a safety razor, is an instrument having asharp razor blade, such as in a cartridge disposed on a handle, inconjunction with a shave preparation product such as water typicallyapplied to the skin in combination with a shaving cream, gel or lotion,to shave hairs on the skin.

It is a further object of the invention to provide a method of measuringskin strain on the external skin of a person while applying a force tothe skin, such as by a finger or blunt probe object dragged along aportion of skin to which a cosmeceutical product, such as a lotion,cream or emollient, has been applied.

In one aspect, the invention features a method of measuring a parameterindicative of deformation of skin surface of a living person resultingfrom a force applied to the skin surface during the test. The skin ofthe person being tested is first provided with a pattern and then isimaged by two digital cameras. The cameras then capture reference imagedata of the undeformed or reference position of the patterned skinsurface. While applying a force to the skin, the cameras capture secondimage data indicative of the deformed position of the patterned skinsurface. The reference data and stressed or deformed condition data isstored and processed to determine movement of the patterned skin surfacerelative its reference position. At least one parameter indicative ofthis movement (“deformed state”) of the patterned skin surface relativeits reference position (“undeformed state”) is determined. Preferablythat parameter is a numerically quantifiable parameter. More preferablythat parameter is a strain. The parameter determined can be a straintensor or a strain rate. The parameter determined can be major strain orminor strain. The parameter determined can alternatively be positionalcoordinates, displacements, speed, or acceleration of the skin.

In certain implementations of the method: The force applied to the skincan be from shaving, or by a finger or blunt probe drawn across theskin. A performance characteristic of a razor can be quantified such asthe strain produced in the skin surface during use. Comparisons can bemade between razors or a prototype evaluated during development. Anefficacy of a cream or lotion applied to the skin can be evaluated.

Advantageously in certain implementations of the method, the quantity ofthe movement, such as an amount of strain during shaving with a razor,can be determined over several different measurement areas of theshaving stroke. An average strain can be determined for each measurementarea. This advantageously allows quantifying performance of a razor overa representative range of its intended use. An overall average strainquantity can be determined from the several measurement areas.

Advantages of the present invention include that the optical measurementsystem is not invasive to the user, it does not touch the test person'sskin not interfere with normal motion using a product that applies forceto the skin. Another advantage of the inventive method is that allowsthe test person to freely move his or her body and act in a normal,unconstrained manner, thus more realistic replicating conditions ofnormal use, since translational or so-called rigid body motions aresubtracted out and do not distort the measurements. The test subject canshave himself or herself, or draw the finger (or blunt probe) across theskin, or another a test administrator can apply the force to the testsubject.

The pattern applied to the skin can be a regular pattern or a randompattern. A random pattern is also referred to as a stochastic pattern.The pattern can be applied as a multitude of “dots” to the test person'sskin.

In another aspect, the invention features a prepared pattern that iseasily applied to the skin of a test subject and is also removable afterthe optical measurements. A removable tattoo is provided with asubstrate and a pattern having a plurality of indicia randomlydistributed to form a pattern density of between about 40% and about60%. In advantageous embodiments the indicia is in the form of dots.

In another aspect, a tattoo to pattern the skin for optical measurementsis provided having a substrate and a random pattern (45) having aplurality of distributed dots. The dots are made with an ink or dye thatis substantially water insoluble but is substantially soluble in analcohol. The substrate can be moisture permeable, e.g. to alcohol.

In advantageous embodiments the individual elements that make up theindicia or dots have two different sizes. In further embodiments thereare three, or more, different sizes present in the pattern.

In further advantageous embodiments, the removable tattoo has a patterndensity of about 50%. In other, presently yet more preferredembodiments, the pattern density is about 42.5%.

In further embodiments the tattoo is transferable to the skin by wettingwith an alcohol. The substrate can be a paper, such as paper commonlyreferred to as blotting paper or cigarette paper. The tattoo can beprinted with an oil-based ink or dye.

The tattoo is preferably made convenient by being devoid of a coverlayer formed above the pattern on the tattoo, thus obviating the need topeel off such a layer before applying it to the skin. The tattoo is alsomade convenient and economical to manufacture by being devoid of anadhesive layer.

Further embodiments are disclosed in the dependent claims attachedhereto.

The present invention and its advantages will be better understood byreferring, by way of example, to the following detailed description andthe attached Figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic view of a prior art image analysis system;

FIG. 2 shows a schematic view of an imaging system of FIG. 1 employed ina method of measuring the skin according to one embodiment of theinvention;

FIG. 3 shows a perspective view of the image system of FIG. 1;

FIG. 4 shows a schematic representation of a digital optical imageillustrating pixels and facets in an undeformed state;

FIG. 5 shows a schematic representation of a digital optical imageillustrating pixels and facets in a deformed state;

FIG. 6 shows a flowchart of optical image analysis steps;

FIG. 7 shows a preferred stochastic pattern transferable to the skin foruse with the method employed in FIG. 2;

FIG. 8 shows an optical image of the reference pattern on the skinemployed in a method of measuring the skin according to one embodimentof the invention;

FIG. 9 shows a schematic view in grey scale of skin strain at amid-stroke shaving position;

FIG. 10 shows a schematic view in grey scale of skin strain at anend-of-stroke shaving position;

FIG. 11 shows a schematic view in cross-hatching scale of skin straincorresponding to FIG. 9;

FIG. 12 shows a schematic view in cross-hatching scale of skin straincorresponding to FIG. 10;

FIG. 13 shows a schematic representation of a strain measurement areanear start of stroke;

FIG. 14 shows a schematic representation of a strain measurement areanear mid-stroke;

FIG. 15 shows a schematic representation of a strain measurement areanear end-of stroke;

FIG. 16 shows a blunt probe employed in a method of measuring the skinaccording to another embodiment of the invention;

FIG. 17 shows a reference diagram depicting translation and strain of aline element;

FIG. 18 shows a reference diagram depicting a geometrical model ofcentral projection;

FIG. 19 shows a reference diagram depicting an analytical calculation ofthe deformation gradient tensor;

FIG. 20 shows a reference diagram depicting a 3×3 neighborhood forstrain calculation;

FIG. 21 shows a reference diagram depicting a neighborhood for afour-sided facet; and

FIG. 22 shows a reference diagram depicting a four-sided facet withadjacent points.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION TheImaging System

Reference is made to FIGS. 1-3.

For the 3D deformation and strain measurements, sample 35 (shownschematically in FIG. 1) to which forces should be applied (whichaccording to the invention as shown in FIG. 2 is an external skinsurface of a living person 40, for example during shaving), is viewed bya pair of high resolution, digital CCD cameras 10, 20, which measure thesample's 3D coordinates and the 3D deformations. The camera pair issimply placed in front of the object being tested at a working distance30. A typical working distance is 1 meter to 2 meters. The 3D imagecorrelation photogrammetry technology is a combination of two-camerasynchronized image correlation and photogrammetry. A regular pattern ora random pattern 45, with good contrast, is applied to the surface ofthe test object, such as to the surface of the skin, which deformsduring the test. While a regular pattern can be used, such as an arrayof dots aligned in repeating columns and rows (such as a rectangularlattice), a random pattern is preferred so as to avoid a situation thatcould theoretically occur with a periodically repeating or regularpattern that a deformation occurs in an integer amount of the pattern,such that the camera might mistake such a deformation for a massive orrigid body translation. The random pattern does not have to beabsolutely random in a strict or mathematical sense such as from arandom number generator, it is sufficient that the pattern is notperceptibly a periodically repeating pattern. The deformation of thispattern under the applied load conditions (which according to anembodiment of the invention is the act of shaving) is recorded by theCCD cameras and evaluated. The initial image processing defines uniquecorrelation areas known as macro-image facets, typically 5-25 pixelssquare, across the patterned imaging area. Each facet center is ameasurement point that can be thought of as an extensometer point andstrain rosette. These facets are tracked in each successive image withsub-pixel accuracy (to 100^(th) of a pixel). Then, using conventionalphotogrammetric principles (such as discussed in Mikhail, E., Betel, J.,and McGlone, J., Introduction to Modern Photogrammetry, John Wiley andSons, 2001, which is hereby incorporated in its entirety by reference),the 3D coordinates of the patterned surface of the specimen arecalculated. The results are the 3D shape (contour) of the component, the3D displacements, and the plane strain tensor of every point on thepatterned surface of the object.

The 3D image correlation tracks changes in the applied micro-pattern(stochastic pattern), rather than a projected pattern, and uses ordinarywhite light, rather than coherent laser light. The system tracks thepattern applied to the measurement surface with sub-pixel accuracy. Thismeans that as long as the object remains within the field of view of thecameras, all of the local deformations can be tracked. Thus, largedeformations can be analyzed in a single measurement. Rigid body motiondoes not affect the measurements, and can also be calculated from theoriginal pixel registration. Indeed, measurements can be continued afteran object being studied has been removed, processed and replaced withinthe camera viewing zone.

Sensitivity with 3D image correlation is 1/30,000 the field of view. Forexample, with a 3 cm field of view, sensitivity is 1 micron, and with a30 cm field of view, it is 10 microns. A field of view of several meterssquare is not a problem as long as deformations of several 10's ofmicrons are present. The system intrinsically measures 3D shape, andtherefore 3D deformations are measured simultaneously, rather thansequentially.

An example of a commercially widely available 3D image correlationphotogrammetry digital camera system to obtain the foregoing results isthe system made by the company GOM mbh (“Gesellschaft fuer OptischeMesstechnik”) (address: Mittelweg 7-8, D-38106 Braunschweig, Germany;website www.gom.com) marketed under the trade designation ARAMIS systemand described in their publication “ARAMIS User Manual v5.4.1 (year2005), which is hereby incorporated in its entirety by reference; thisARAMIS system is widely distributed in the United States such as by thecompany Trilion Quality Systems (address: Four Tower Bridge, 200 BarrHarbor Drive, Suite 400, West Conshohocken, Pa. 19428; websitewww.trilion.com), which is the system described in the above“Background” section in use for example in the aerospace industry, theuniversities and NASA, and in the technical literature therein. Thissystem permits a large measuring area, since with the same sensor bothsmall and large objects, such as those in size from 1 mm to 2 meters,can be measured, and strains in the range of 0.05% up to several hundred%. FIG. 1 schematically illustrates such a system.

The left camera 10 has a left camera lens 11, and the right camera 20has a right camera lens 21. The cameras are each connected to a cameraadapter plate 13 and mounted to a camera support 15 such as a railsupported by a camera tripod 16. For adjustment, the cameras can rotatetheir camera rotation axis 12, which are separated from each other bybase distance 25. The cameras 10, 20 are located to the left and right,respectively, of angle bisector 24 generated by a laser pointer 28 thatbisects the camera angle α (“alpha”) at which the cameras are directedto the specimen (35, 40) to be measured. Laser pointer 28 is used onlyfor calibration to align cameras 10, 20, it is not in use duringmeasurement of the strain such as when the test subject is shaving.

Object 35 to be measured is located at an approximate center 34 within ameasuring volume defined by a width W, height H and a length L.

In operation, the system is a non-contact optical 3D deformationmeasuring system, as illustrated in FIG. 1 or FIG. 2. It analyzes,calculates and documents deformations of the skin surface. The graphicalrepresentations of the measuring results provides an understanding ofthe behaviour of the skin surface to be measured. The system recognizesthe surface structure of the object to be measured in digital cameraimages and allocates coordinates to the image pixels. The firstcoordinates are already gathered when recording the reference conditionswhich represents the undeformed (for example, an unstressed skincondition prior to the shaving action) state of the skin surface. Afteror during the deformation to the skin surface to be measured, furtherimages are recorded. Then, the system compares the digital images andcalculates the displacement and the deformation of the skin surfacecharacteristics relative to the reference image. The system is suitablefor 3D deformation measurements under static and dynamic load in orderto analyze deformations and strain of real components.

A typical set-up of hardware components is illustrated in FIG. 3. Asuitable arrangement of hardware and software components to operate themeasurement system includes: a pair of 1.3M cameras (10, 20) with 50 mmlenses (11, 21) connected to a computer via a “Firewire” connection(Apple Computer, Inc.'s trade designation of its widely availableIEEE-1394 interface, a computer and digital video serial bus interfacestandard); and a 64-bit dual processor computer (18) with a Linuxoperating system and Aramis application software version 6.0.0-4(software is periodically updated by its manufacturer GOM mbH). Thecameras are assembled and sold by the company GOM using commerciallyavailable 50 mm lenses from Schneider (Jos. Schneider Optische WerkeGmbH of Bad Kreuznach, Germany), but other 50 mm lens can also be used.The designation “1.3 M” indicates a nominal 1.3 Megapixels, for examplea camera resolution of 1280×1024 pixels for each image.

The typical frame rate for the camera system is 10 fps (“frames persecond”, referring to the still frames per second). This frame rate wasdetermined to be adequate for all or most all of the test subjectsexcept a test subject who shaved exceptionally fast. It is understoodthat typical video has a frame rate of about 30 fps, and that thedesignation “high-speed” can range from 480 fps to 80,000 fps. Othercameras are available for the system that are higher resolution (4M) butat a lower frame rate (max 7 fps) or a higher speed (480 fps). The framerate as “fps” can also be expressed in terms of Hz, e.g. 12 fps=12 Hz.

To make measurements, the measuring volume is selected. For a human face40 or leg a suitable selected volume for the camera and lensconfiguration used here is approximately 135 mm×108 mm×108 mm. Thecalibration of the system utilizes a certified calibration plate basedon the selected volume. Volumes ranging from 10 mm³ to 1000 mm³ arepossible, and are chosen depending on the size of the skin area tomeasure.

A suitable set of system components is shown in the table below:

System 1.3 M camera Facial measuring volume with 50 mm 135 mm × 108 mm ×108 mm lens Camera resolution 1280 × 1024 pixels Camera chip ⅔ inch CCDMax. frame rate 12 fps Shutter time 0.1 ms up to 2 s Strain measuringrange 0.05% up to 100% Strain accuracy up to 0.02% Displacementsensitivity 6 microns

Instead of the CCD cameras, it is also possible to use suitable CMOScameras, which are believed to have similar parameters.

While the above described camera speed in the range of 10 to 12 fpspreferred, the camera speed is not critical; one of skill in the artwill appreciate that it is possible to use a camera speed of severalthousand frames per minute, e.g. 70,000 fps, and that one simply needsenough speed to capture enough strain pictures. One of skill in the artappreciates that the practical limits of frame speed are determined bythe computer memory (RAM) and the “Firewire” interface, such that thenumber of pixels decreases with increasing frame speed, and that thefewer pixels that are present then the lower the resolution possible.

A typical procedure for making measurements involves the followingsteps:

1. Applying a stochastic pattern to the surface of the skin area ofinterest, such as via a temporary tattoo design (described furtherhereinbelow);2. capturing a reference image in the form of synchronized stereodigital images;3. applying shaving preparation (e.g. shave cream) to the area ofinterest (for shaving applications). Some of the patterned dots are leftfree of shave prep so that the computer can relate to the referenceimage;4. capturing a series of frames in the form of synchronized stereodigital images that encompass a stroking motion of the razor; and5. analyzing the series of captured images using the evaluation mode ofthe Aramis system software, which recognizes the applied pattern on thereference image and subsequent strained images. The 3D coordinates, 3Ddisplacements and the plane strain tensor are calculated usingphotogrammetric evaluation, and the results graphically displayed.

In order to analyze the images, the operator identifies a start point inthe images. The area to be evaluated (computation mask) and the startpoint are defined directly in the camera images. The software thencalculates square or rectangular image details or boxes, which arecalled facets, over the patterned area. Preferably the pattern appliedto the surface being observed is smaller than the facet size. Each facetcan be chosen to be made up of, for example, about 15 pixels×15 pixels.To improve resolution, the facets can have an overlap area, for examplea 2 pixel overlapping area can be suitable for stationary objects suchas those that are fixtured. It has been determined that for analyzing ashaving action it is suitable to chose a facet to have a 25 pixel square(25×25 pixels). It is preferred with facets of this size to use anapproximate half-facet size overlap, that is a 13 pixel overlappingarea. This helps with accuracy during shaving, where the test subject ismoving, in order to cover more points with the facets. In the summaryflowchart of FIG. 6 these steps are referenced in operation blocks 1 and2.

The facets will be explained with reference to FIGS. 4 and 5. FIG. 4shows an example of pixels 50 defining rectangular-shaped facets, eachpixel 50 being the smallest unit and represented as a square or box. Thepixels have individual gray levels. FIG. 4 shows an exemplary pair offacets (15×15 pixels) of the left camera 10 and of the right camera 20.FIG. 4 reflects the applied pattern in an unstressed state, thus formingthe image for the undeformed reference state. FIG. 5 shows an example ofthe facets shown in FIG. 4 having been deformed after the patternedobject is taken through successive, intermediate deformation stages (notshown) to a final deformation state (“stage F”). The black quadrilateralin FIG. 4 and FIG. 5 superimposed on the pixels 50 illustrates the facetin the undeformed state. As seen in FIG. 4 in the undeformed state, theleft camera 10 contributes the left image upon which facet 52L isconstructed, and the right camera 20 contributes the right image uponwhich facet 52R is constructed. The facet from left camera 10 appears asa square, while the facet from right camera 20 appears tilted resemblinga trapezoid, since, relative to the left camera 10, the right camera 20is focused on the same region of the object, e.g. face 40, but is takinga picture at an angle α to the left camera 10.

As seen in comparison in FIG. 5, on the deformed patterned object, thefacets 52L, 52R have undergone deformation and are shown in dashed linesas deformed facets 54L, 54R, respectively. For convenient comparison,the undeformed facets 52L, 52R are also shown on FIG. 5.

The steps taken in the image processing in order to calculate major andminor strain are summarized in the flowchart of FIG. 6.

A reference condition is compared to a series of deformed conditions.The Aramis system software determines the 2D coordinates of the facetsfrom the corner points of the facets and the resulting center of eachfacet. Using photogrammetric methods, the 2D coordinates of a facet,observed from the left camera 10, and the 2D coordinates of the samefacet, observed from the right camera 20, lead to common 3D coordinatesof each corner and center of each facet. (This is referenced inoperational block 3 of the flowchart in FIG. 6). The change in thesecoordinates as the surface is strained is measured for each subsequentimage pair (left-right) and the deformation relative to the referenceimage is calculated. The values are reported as various displacement andstrain values. For the measurement of shaving it is preferred to report“major strain” as a percent change (% change). The major straindirection follows the razor as it passes over the skin so this isbelieved to be the most relevant parameter for studying shaving.

The facets act as virtual strain gauges. Each facet can be thought of asa virtual 3D extensometer. An array of facets acts as a virtual strainrosette; this is an approximate analogy since a strain rosette isusually considered as 2D, whereas the facets are 3D. With respect to afacet in its undeformed and deformed states, the difference in tensorlength is calculated by looking at the change in length of the legbetween the deformed state and the reference state, and expressed as apercent (%) change. Because the coordinates that are determined are in3D from a curved surface, they are translated first into 2D using atransformation (such as a spline model, as referenced in operationalblock 4 of the flowchart in FIG. 6) and then applying engineering straincalculations. With reference again to the flowchart of FIG. 6, as shownin operational block 5, the deformation gradient tensors are calculatedaccording to the known relation:

p _(v) =u+F·p _(u),

where

-   -   p_(u)=the coordinates of a reference point    -   p_(v)=the coordinates of the deformed point    -   u denotes rigid body translation.        As noted in operational block 6, the major and minor strains are        derived from the deformation gradient tensor. The primary        direction is the major strain. For background information, the        basic strain relations are discussed in the Appendix at the end        of this application's specification.

Because rigid body motion that is seen by both cameras is subtracted outin accordance with the above relation, then any inadvertent motion of atest subject, while shaving, for example moving his head or body withinthe field of view of the cameras (or even walking within the field ofview), does not detract from imaging the strain in the skin due to therazor's shaving action. This analytic technique is well suited tomeasure strains in the skin as they occur when a person shaves himselfor herself in normal use, without having to unnaturally constrain thetest subject.

If a person has very coarse beard hair, that may also be recognized bythe imaging system as a pattern; that is not a disadvantage since beardhair grows in an irregular pattern.

Comparing Shaving Characteristics

A reference image is shown in FIG. 8, which illustrates a digital imageof pattern 45 prior to shaving (the dark, somewhat jagged line boundingpattern 45 is an artifact of cropping the image to enhance visibility).The image shows a generally strain-free, unloaded condition of theshaving surface.

The strain patterns on the skin being shaved are illustratedschematically in FIGS. 9-12. FIG. 11 is a cross-hatched version of thegray-scale image in FIG. 9. FIG. 12 is a cross-hatched version of thegray-scale image in FIG. 10. The strain in the areas behind the razor isrepresented by bands or regions of similar magnitude, as depicted by theregions of similar shading, with the scale “% Major Strain” showing thecorresponding scale for the shaded region. The Aramis imaging systemprovides these bands in color, and they are superposed over the blackdots of the reference image shown in FIG. 8; however, the strain bandsare rendered herein in grey scale (and with the black reference dotsremoved) in FIGS. 9 and 10, and schematically in cross-hatch in FIG. 11and FIG. 12, for convenience of photo-reproduction and printing onpaper. The corresponding color is also indicated on the legends in FIGS.9-12.

FIG. 9 shows an image of the face being shaved over skin with pattern 45with blade unit 77 positioned at about mid-stroke. FIG. 9 shows themaximum strains present in bands (100, 101, 102, 103, 104) in therespective skin surface portions that have been shaved. In FIG. 11 thestrain bands (100, 101, 102, 103, 104) are depicted using differentcross-hatching to indicate the several strain levels. For example, themesh formed by intersecting vertical and horizontal lines indicates astrain level between about 6% and 8% in band 101; on a color imageavailable from the Aramis system that band would be indicated with e.g.a yellowish color. It will be noted that the higher strain levels areseen closer to behind the razor, such as in strain band 104. It will beappreciated that the commercially available Aramis system generates acolor image in which the colored bands or regions tend to blend into oneanother, for example a slightly higher strain region is indicated withe.g. a light green color, and the yellowish colored lower strain regionblends with a somewhat diffuse border into the next higher strainregion, and there is also present the black reference dots shown in FIG.8. Such a light green higher strain region corresponds in FIG. 11 to thecross-hatching of downwardly slanted alternating solid and dashed linesused to represent the strain band 102 between about 8% to 10%. In FIGS.9-12 the grey scale or cross-hatching depictions schematically indicatethat the various strain regions lie next to one another, and, asmentioned, the black reference dots of FIG. 8 have also been removed tofacilitate clarity. As seen in FIG. 9 (or FIG. 11), there are about five(5) readily identifiable bands (100, 101, 102, 103, 104) of differentstrain magnitude. Each of FIGS. 9 and 11 illustrates in a region justbehind the razor a strain level of between about 12% but less than 14%major strain as the highest strain band 104 on that image, indicated inFIG. 11 with the cross-hatching that is upwardly slanted alternatingsolid and dashed lines (to represent a turquoise color on an image fromthe Aramis system, as indicated on the legend).

FIG. 10 shows an image of the face being shaved over skin with pattern45 with blade unit 77 positioned at about the end of stroke. The imageof the type shown in FIG. 10 is about ten (10) images subsequent to theimage of FIG. 9. As shown in FIG. 10, since the image capture is dynamicthe previous strains that were present in the region depicted in FIG. 9have decreased since the razor has moved further away from the FIG. 9region and is not pulling it as much, since that region (“midstroke”,designated approximately with bracket 60 in FIG. 10) is now furtherbehind the razor as the razor has advanced lower on the face towards thejaw. As seen in FIG. 10, there are eight (8) readily identifiable bands(100, 101, 102, 103, 104, 105, 106, 107) of different strain magnitude.FIG. 10 illustrates a region just behind blade unit 77 of strain above18.5% major strain in band 107. This is illustrated in FIG. 10 by bandsof darker grey shading than are seen in FIG. 9. In FIG. 12 the strainband 107 corresponding to the highest strain band seen in FIG. 10 (above18.5%) is indicated with vertical dashed lines (to represent a violetcolor on an image from the Aramis system).

Image analysis is explained with reference to FIGS. 13-15. It isunderstood that the analysis depicted relative to FIGS. 13-15 isperformed on the images shown in, for example FIG. 10, or equally inFIG. 12 upon completion of shave stroke. For convenience to show thetechnique of defining representative spatial regions, FIGS. 13-15 omitthe depictions of the bands of strain and reference dot pattern 45. Toanalyze the images, a group of images is selected that starts just afterthe shave stroke has begun and ends approximately near a line extendingback from the lip (with respect to images collected when shaving theface). Sometimes a pair of images, that is images from the left andright cameras 10, 20, is referred to as a “stage” or “rendered image”since it reflects a 3D rendering calculated from the left and rightcamera individual digital pictures, but for simplicity each “stage” isreferred to as “image”. Within that set of images, an area just behindthe razor is selected, and the average strain in that area is recorded.The “area behind the razor” is meant in the sense that it trails therazor, in that that area has just been shaved and the razor has movedpast it, exposing it to be imaged.

As shown in FIG. 13, an imaginary start line 75 is constructed from thenose to the ear. FIG. 13 depicts an approximate start-shaving position.An imaginary end line 76 is constructed approximately parallel to startline 75 extending backwards from the lip. As the razor blade unit 77 isdrawn past start line 75 a first measurement area 80 is chosen on theimage seen in FIG. 12. The measurement area 80 is chosen to beapproximately the size of blade unit 77, and located just behind theblade unit (“behind” in the sense of being opposite the direction ofrazor travel during the shaving stroke). It is understood that theimaginary lines 75 and 76 and reference measurement area 80 areconstructed over the strain bands image resulting for example in FIG. 11or 12, omitted here for easier depiction. Since measurement area 80 isconstructed over the strain bands in, for example, FIG. 11, the softwarein the Aramis system selects and averages the strains within thatbounded measurement area 80 and reports the average major strain in thatmeasurement area 80. It will be understood that within a measurementarea, instead of the average strain, other parameters indicative ofshaving performance could be chosen; for example, it is possible toinstead calculate the minimum strain, or the maximum strain, and thestandard deviation.

As shown in FIG. 14, the user has drawn the razor further down towardsthe jaw, and blade unit 77 is approximately at a mid-stroke position.For illustration purposes, the previous start position in FIG. 13 isindicated with a phantom-line blade unit 77′. FIG. 14 illustrates how asecond measurement area 81 is chosen at this position, behind blade unit77, within which the average strain is calculated.

As shown in FIG. 15, the user has drawn the razor further down such thatblade unit 77 is approximately at an end-of-stroke position, prior tothe user beginning to lift the blade unit away from the skin. A thirdmeasurement area 82 is chosen at this position, behind blade unit 77,within which the average strain is calculated. Any desired number ofmeasurement areas can be provided between beginning of stroke and end ofstroke; it is presently preferred to use four such measurement areas.The selected measurement areas can be adjacent to one another and it isalso acceptable if they are slightly overlapping.

Four measurement areas selected as with the exemplary measurement areas80, 81, 82 were selected from the set of images so as to be distributedover a reasonable amount of the distance of the entire shave stroke, andthen their individual averages were averaged together. It is preferredthat the four such measurement areas be distributed so as to cover thedistance from a start of stroke to end of stroke over a reasonablelength of stroke before the user starts to lift blade unit 77 off theskin. For example, over the overall shave stroke between start- andend-of-shave there may be between eight (8) and twenty (20) images, withtwelve (12) images being common; this varies based on stroke speed. Four(4) images that encompass the strain just behind the razor over thetotal area were selected, approximately every third or fourth imagebased on 12 images overall, and corresponding measurement areas selectedand their average strains calculated. It is understood that anothernumber of measurement areas, e.g. a number more than four, could havebeen selected between the start and end of shave stroke.

Comparative razor testing: These images provide a quantitative tool tocompare the performance characteristics of different razors. Whencomparing razors, one looks at the difference in average % major strainover the stroke area. It is also understood that if in the measurementareas 80, 81, instead of major strain, the maximum strain or the minimumstrain or the standard deviation have been evaluated, then one wouldlook at differences in the maximum strain or minimum strain or standarddeviation. In this manner a strain exerted on the skin produced by twodifferent razor blade units can be compared. It is also possible toevaluate differences between a test and a control blade unit that has adifferent feature in the blade unit, such as a different guard, or eventhe same blade unit mounted on different handles to test performancedifferences possible owing to the ergonomics of a handle. Such testingcan assess differences between existing razors or facilitatedevelopmental testing of prototype razors.

A comparison was made between two razors manufactured by the assignee ofthe present application, The Gillette Company, (Boston, Mass., USA),namely razors marketed to male consumers under the trade designations“Fusion” and “Fusion Power”, each widely commercially available in theU.S. market since late 2005, and in other markets. Each of the “Fusion”and “Fusion Power” razors is a safety razor whose cartridge has fiveblades on its primary shaving surface positioned between a guard at thefront and a cap at the rear. This razor cartridge is shown in assignee'sU.S. Pat. No. 7,131,202 (Pennell et al.), which is hereby incorporatedby reference, in particular in FIGS. 1-3 therein.

The manual “Fusion” razor is depicted for example in assignee's U.S.Design Pat. D534,313 (Provost et al.), hereby incorporated by reference,and in U.S. Pat. No. 7,131,202 at FIGS. 1-2, and is also seen in FIGS.9-15 of the present application (without in any way limiting thegenerality of the measurement procedure). This version “Fusion” razor isreferred to as “manual” in the sense that the motion occurs from themanual action of drawing the razor across the skin and it does not havea motor on the razor exciting additional blade motion.

The “Fusion Power” razor is depicted for example in U.S. Design Pat.D534,315 (Provost et al.) and in pending patent application U.S. Ser.No. 11/220,008 filed 6 Sep. 2005 (Schnak et al.) (to publish as US2007/______A1), which are both hereby incorporated by reference. This“Fusion Power” razor is referred to as a “power” version razor sincethere is a power source (e.g. a battery) as well as a motor driving aneccentric weight (also called flyweight) located in the handle that,when energized, causes during shaving use small amplitude oscillation ofthe razor cartridge that is connected to the handle.

A comparison was made to determine whether the “Fusion Power” razor inshaving use exhibits less drag than a “Fusion Manual” razor. Each razorwas used in its normal, intended operational manner, that is, duringshaving the “Fusion Power” razor was energized so that it vibrated. Themajor skin strain was measured on the x-, y- and z-axes. Twenty-fivetest panelists shaved following a 24-hour hair growth period, and thestrokes were measured during shaving. Differences in major strain weredetermined between the two razors. For the manual “Fusion” razor theaverage major strain measured was about 14.3%. For the “Fusion Power”razor the average major strain measured was about 13%. This shows adifference of at least 9% lower strain when using the “Fusion Power”.

Other Skin Applications

It is understood that the aforementioned analysis technique can beapplied to other applications of a stressing force applied to the skinto determine a response characteristic in the skin. For example, onecould measure strain on the skin as hair is being plucked out forexample using an adhesive tape lifting or wax depilatory strips, as anexample of testing hair epilation products.

It is theorized that a cleanser agent applied to skin dries out theskin, that the skin thereby would become stiffer or otherwise bereferred to as less supple. It is thus hypothesized that, in thepresence of the same force as applied to skin that has been treated withthe cleanser as compared to that skin not treated with the cleanser,then in the cleanser-treated skin there will be less strain since theskin is stiffer. If a moisturizing agent is applied to make the skinsofter or more supple, then in the presence of the same force suchmoisturizer-treated skin would yield more and show a higher strain.

In optical image testing of the effect on the skin of a moisturizingproduct, such as a lotion, cream or emollient, having been applied, itis suggested that a finger of a person or as shown in FIG. 16 a bluntprobe object 90 (which emulates a finger) be dragged along a portion ofskin during the test in order to transmit a force to the skin. Probe 90has a suitable radius at its tip to be generally smoothly dragged acrossthe skin. The force applied can arise not only from an externallyapplied force such as a finger or probe 90, but also from internallycaused forces; for example, a test subject can be asked to flex amuscle, such as smiling, frowning or making a facial expression, inorder to apply a force to the skin and measure the skin deformation.

The Temporary Tattoo Pattern

One of skill in the art appreciates that for imaging the skin whileshaving, the pattern should desirably not be damaged by exposure to theshaving environment, typically involving water and a shave prep such assoap or a shave cream or gel, and it is also desired that the patternnot be permanent but be generally readily removable from the skin uponthe conclusion of the test. Also, in general, if the skin is exposed toa lotion such as a moisturizer as part of testing and imaging, a patternshould be applied that will not be readily smudged by the material beingtested.

In order to pattern the skin surface to have a suitable target togenerate the reference and deformed images, the skin of a subject waspainted by hand by stippling the paint to the cheek with a narrow paintbrush so as to create “dots”. A water-insoluble paint was chosen such asa commercially available paint from a hardware store, for example theoil-based enamel paint sold in the United States under the tradedesignation “Rustoleum” in the color black. Dabbing this paint with thepoint of a fine-tip paint brush to the skin gave a random pattern ofdots of high contrast which gave suitable results during the imaging andanalysis. This method of applying the skin pattern with paint had thedisadvantages, however, of a strong odor, being messy, exposing theperson to excess paint, requiring careful preparation that wastime-consuming, and being inconvenient to remove from the skin. While aspray paint technique could possibly be used such as a spray paint canby intermittently depressing the can's button, or using an airbrushtechnique, to more quickly give a suitable random pattern, in order toadequately protect a person's eyes, nose, ears, hair and clothing duringsuch an application would require elaborate masking of those areas, andcould still expose the person to excess paint spray or fumes, and wouldthus also be inconvenient.

In order to provide a pattern 45 that could quickly be applied to a faceor body surface to be shaved and imaged, a transfer pattern wasdeveloped, as shown in FIG. 7. The pattern 45 can be prepared as atemporary body tattoo printed with standard FDA-approved ink as shown inFIG. 7 and easily transferred to the skin surface. The tattoo pattern 45is removable or temporary, as those words are used herein, in that thepattern 45 can be wiped off or removed from the skin on which it hasbeen applied such as by alcohol or by vigorous, normal washing withwater and conventional soaps, make-up or cosmetic removal compositions(such as petroleum-based lotion), and the like. While the presenttemporary tattoo may be removed with repeated washings with soap andwater, it is more quickly removed by use of an alcohol. The presenttemporary tattoo is contrasted with permanent tattoos which cannot bewiped off or removed by washing, and can only be removed by medicalintervention or the like, such as by laser or surgical means.

The skin is first cleaned, for example with 70% isopropyl alcohol, andthe transfer paper 73 applied to the skin area to be patterned. Thetransfer paper 73 is wetted with alcohol to transfer the ink pattern 45.It has been determined that the ink used is resistant to removal withwater, resistant to the shave preparation used (e.g. shaving soap, foamor gel), and resistant to the act of shaving itself (e.g. the action ofrubbing the cartridge over the skin or the blades moving over the skin),and yet the transferred pattern is advantageously easily removable withalcohol at the conclusion of the test.

It was found convenient to create pattern 45 shown in FIG. 7 as acomputer data file using a commercially available desktop publishingsoftware such as Adobe Photoshop. Pattern 45 has indicia distributed ina random pattern. It is preferred that the indicia be three differentsize dots in a generally random distribution. The diameters of therespective dots are: small dots 70 of 1.6 mm (0.063 in), medium dots 71of 2.1 mm (0.083 in), and large dots 72 of 2.6 mm (0.103 in) diameter.It is not required that the dots be precise circles having amathematically true diameter, the dots can be of a non-circular orarbitrary shape, such as small ovals or ellipses, or even smallpolygonal shapes including rectangular. The distribution of the dotsizes in the overall pattern is approximately one-third each size. Thepattern 45 could be fashioned of just two different dot sizes; however,three different dot sizes is preferred. Pattern 45 can comprise morethan three different dot sizes. Pattern 45 with this size distributionis small enough to allow a good raster of calculation facets duringevaluation, and it also large enough to be resolved by the camera. (Theimage of FIG. 7 is printed out as a square of 5 inch×5 inch)

It is preferred that the density of pattern 45 be in the range of about40% to about 60%. The lower approximate “40% density”, for example,means that for a given square area of pattern 45 about 40% is occupiedby the darker image (e.g. the dots, collectively) and 60% occupied bythe background space. The background, in order to give sufficientcontrast, is neutral or so-called “white” space. The upper approximate“60% density”, for example, means that for a given square area ofpattern 45 about 60% is occupied by the darker image (e.g. the dots,collectively) and 40% occupied by the neutral (“white”) space. Anapproximate midrange value of about 50% pattern density is believed togive good results. In the preferred embodiment, pattern 45 shown in FIG.7 was suitable in practice with a pattern density of about 42.5% (thusthe remaining “white” space comprises about 57.5%). Pattern 45 ispreferably of a consistent pattern density over its extent, thusfacilitating applying it to the skin surface such as a cheek or leg.

The pattern 45 is printed on a substrate 73. Substrate 73 can also bereferred to as a web or release web, since in the art of transfertattoos it is known that the web releases printed pattern 45 to transferit to the skin. Substrate 73 is preferably moisture-permeable (moistureabsorbing, such as absorbing an alcohol); this assists in releasing theprinted pattern when the substrate is placed against the skin and wettedwith alcohol (e.g. isopropyl alcohol or denatured alcohol). Preferablysubstrate 73 is made of paper or cellulose material. It has been foundconvenient to use as substrate 73 what is referred to in the paper artas “blotting paper” or cigarette paper of the type commonly sold forrolling one's own cigarette. Other substrates could include paper suchas Kraft paper, plastic, or composites thereof. The pattern 45 can begenerated on substrate 73 in a long roll similar to wallpaper orgift-wrapping paper, preferably pattern 45 has a consistent patterndensity over at least a length dimension of a size of a cheek, at leastabout 4 inches (approx. 10 cm), which facilitates application to thecheek.

The dots of pattern 45 are printed with inks. It will be appreciatedthat inks used are suitable for skin contact and are non-toxic such asthose approved for food, drug and/or cosmetic use (“FD&C” or “D&Cgrade”) in the United States. Such inks are mentioned in the U.S. Codeof Federal Regulations at 21 C.F.R. Parts 73 and 74. These are generallyfood grade and/or cosmetic grade inks, being the same colorantsmanufactured in compliance with FDA regulated cosmetics. Suitable inksare pigmented and solvent based. The preferred ink is not water-soluble.A useful black ink is one containing iron oxide, which is a pigment.Dark ink is preferred, such as black ink referred to as D&C Black #2.Such inks are widely commercially available; one such supplier is thecompany Temptu at the address 26 West Seventeenth Street, New York, N.Y.10011 (website www.temptu.com). It is preferred to use inks that aretermed “certified”, meaning certified not to contain toxins. A blue inkcould also be used. Other dark colors or mixtures of ink could also beused. The ink is typically formed of an oil dye or a pigment in acarrier, and is soluble in lower alcohols but has very low watersolubility. The ink or dye is preferably substantially insoluble inwater, but is soluble in alcohol. Such an oil-based ink meets thecriteria of being a temporary tattoo while being sufficiently waterresistant to satisfy the objectives above to provide a pattern to theskin while withstanding the action of shaving. Many such inks are knownin the medicinal and cosmetic arts as suitable for contact with humanskin. Many such dyes are disclosed in U.S. Pat. No. 4,169,169(Kitabatake), the teachings of which are incorporated herein byreference, including at column 3, lines 36 to 68 therein. An oil dye isformulated into an ink composition; in addition to the dye the ink willtypically contain a binder, a solvent, a plasticizer and, optionally,other additives. The thickness of the ink layer of dots 70, 71, 72 willtypically be on the order of 10 microns or less. It will be appreciatedthat the ink layer of pattern 45 deposited onto the skin is extremelythin, and does not affect the skin's characteristics, the shavingperformance or shaving action, and does not interfere with taking themeasurements.

The electronic data file containing pattern 45 can be printed using aconventional computer printer, as is widely commercially practiced, andfor example available from the company Temptu of 26 West SeventeenthStreet, New York, N.Y. 10011. Pattern 45 can be printed onto thesubstrate 73 paper with any known printing process such as offset, silkscreen or gravure to form the temporary tattoo. Also, in order to printthe tattoo, the digitized image or electronic file containing pattern 45can be output from a computer to a conventional ink jet printer or laserjet printer whose ink cartridges have been loaded with D&C or FDAapproved inks and printed onto a paper substrate, as is known in theart. This convenient form of printing is described generally inaccordance with the portion of the teachings directed to printing onto asubstrate as discussed in U.S. Pat. No. 6,042,881 (Ewan), the entirecontent of which is incorporated herein by reference. Other tattooprinting techniques onto a substrate are known in the art field, such asin U.S. Pat. No. 6,596,118 (Bailey), the teachings of which areincorporated herein by reference.

Since an adhesive is omitted, there is no need for a protective releasesheet to cover the finished tattoo. Thus, the indicia of pattern 45 canbe exposed to air during storage, and this further improves theconvenience, simplicity and speed with which test subject persons canhave their skin patterned since there is no protective or cover layerthat needs to be removed and discarded. Furthermore, since the ink usedis not water-soluble, that is a further reason that a protective releasesheet is not needed.

The foregoing specification describes numerous embodiments andvariations showing the wide range of possible constructions andtechniques embodying the present invention. Further variants andembodiments will readily occur to those skilled in the art on the basisof the foregoing disclosure. All such embodiments and variants are to beconsidered as within the scope of the invention as defined by theclaims.

APPENDIX: THE BASICS OF STRAIN

This section explains basics of strain and strain calculation, closelyfollowing the Aramis User Guide (v5.4.1) drawing from the books (listedin the below bibliography) Hibbitt et al.; Becker et al.; Hahn; and Koppet al.

A.1. The Term “Strain”

Strain is the measure for the deformation of a line element and can bedefined as follows:

$\lambda = {\lim\limits_{l\rightarrow 0}\left( \frac{l + {\Delta \; l}}{l} \right)}$

The stretch ratio λ is the relative elongation of an infinitesimal lineelement. A strain value ε can be defined as the function of the stretchratio λ:The following known functions are frequently used strain measures:

-   -   Technical strain:

ε^(T) =f(λ)=λ−1

-   -   Logarithmic or natural strain:

ε^(L) =φ=f(λ)=1n(λ)

-   -   Green's strain:

$ɛ^{G} = {{f(\lambda)} = {\frac{1}{2}\left( {\lambda^{2} - 1} \right)}}$

A.2 The Deformation Gradient Tensor

The above section defined the stretch ratio in the one-dimensional caseand the general description of a strain measure. This will now beextended to the two-dimensional case.

A.2.1 Deformation Gradient Tensor Definition

In order to quantitatively display the deformation of a surface element,the deformation gradient tensor F is introduced. The deformationgradient tensor transforms a line element dX into the line element dx.In both cases, the line element connects the same material coordinates.Theoretically, it is an infinitesimal line element. FIG. 17 illustratesthis case.

Thus, the deformation gradient tensor is defined as:

dx=F·dX

A.2.2 Decomposing the Deformation Gradient Tensor into Polar Coordinates

A disadvantage of the deformation gradient tensor is that rotation andstretch are modeled using only one matrix. This can be compensated bysplitting the deformation gradient into two tensors: a purely rotationalmatrix and a pure stretch tensor. The matrix can be decomposed in twodifferent ways:

-   -   Decomposition into rotation and right stretch tensor        Mathematically, the deformation gradient tensor is decomposed as        follows:

F=R·U

-   -   FIG. 18 illustrates this modeling.    -   Decomposition into left stretch tensor and rotation.        Mathematically, the deformation gradient tensor is decomposed as        follows:

F=V·R

A.2.3 Major and Minor Strain Derived from the Deformation GradientTensor

Values ε_(x), ε_(y) and ε_(xy)=½γ_(xy) can directly be read from thestretch tensor U. It has the following form:

$U = {\begin{pmatrix}U_{11} & U_{12} \\U_{21} & U_{22}\end{pmatrix} = \begin{pmatrix}{1 + ɛ_{x}} & ɛ_{xy} \\ɛ_{xy} & {1 + ɛ_{y}}\end{pmatrix}}$

The strain measures ε_(x) and ε_(y) have the disadvantage of beingdefined as dependent on the coordinate system. This disadvantage can beeliminated by calculating major and minor strain. The symmetrical matrixU can be transformed to the main diagonal form. The two eigenvalues λ₁and λ₂ can be calculated as follows:

$\lambda_{1,2} = {1 + {\frac{ɛ_{x} + ɛ_{y}}{2} \pm \sqrt{\left( \frac{ɛ_{x} + ɛ_{y}}{2} \right)^{2} - \left( {{ɛ_{x} \cdot ɛ_{y}} - ɛ_{xy}^{2}} \right)}}}$

Depending on the choice of the strain measure, the stretch ratios λ₁ andλ₂ can be transformed into corresponding strain values. The largereigenvalue is called major strain¹ ε₁ and the smaller eigenvalue is theminor strain ²ε₂. The corresponding eigenvectors determine the twodirections of major and minor strain. The strain values thus determinedare independent of the coordinate system and are universally applicable.

If the material thickness with respect to the entire surface is small,it is frequently necessary to deduce the remaining material thicknessfrom the deformation of the surface. As the optical measuring techniquesused cannot obtain any data in this dimension, the third principlestrain ε₃ can be calculated from major and minor strain ε₁ and ε₂,assuming a constant volume. Without determining a strain value, therelationship between the stretch ratios can be expressed more generally.The volume constancy can be defined as follows:

λ₁·λ₂·λ₃=1

Frequently, the effective strains are needed. The effective strainsaccording to von Mises and von Tresca are available. The effectivestrain according to von Mises results from the following formula:

$\phi_{V} = \sqrt{\frac{2}{3}\left( {\phi_{1}^{2} + \phi_{2}^{2} + \phi_{3}^{2}} \right)}$

The effective strain according to von Tresca results from the followingformula:

φ_(V)=|φ|max

A.3 Calculation of the Deformation Gradient Tensor from a 2DDisplacement Field

The deformation gradient tensor F is calculated from a given 2Ddisplacement field of points. For this purpose, the 2D coordinates ofeach point must be known both in its undeformed and in its deformedstate. The definition of the deformation gradient tensor F explains howan undeformed line element is transformed into a deformed line element.In order to calculate the deformation gradient tensor for a point, anumber of points in the neighborhood of the observed point is needed.For this model of calculation, a homogeneous state of strain is assumedfor this set of adjacent points.

The deformation gradient tensor creates a functional connection of thecoordinates of the deformed points P_(v,i) with the coordinates of theundeformed points P_(u,i) (i being the index for the different points).The functional connection is as follows:

p _(v) =u+F·p _(u)

with:

p_(u) Coordinates of the undeformed point

p_(v) Coordinates of the deformed point

u Rigid body translation

Reference is made to FIG. 19.

This formula describes a linear system of equations whose unknowns arethe four parameters of the deformation gradient tensor F. Thedeformation gradient tensor F can be interpreted as an affinetransformation which transforms a unit square into a parallelogram. Thissystem of equations can be analytically calculated for three points. Ifmore than three points are chosen, the result is an overdeterminedsystem of equations which generally is contradictory. In this case,methods must be used which permit a calculation with more than threepoints. Thus, the Gaussian least squares adjustment is used.

The number of neighboring points can be adjusted to calculate thedeformation gradient tensor for one point. This thus sets the lengthover which the differentiation is made. The neighborhood for a point isarranged quadratically. The smallest neighborhood is a 3×3 environmentwhich can be increased by an increment of two. FIG. 20 shows a 3×3neighborhood.

For an even higher resolution, the deformation gradient tensor can becalculated for a four-sided facet. A facet consists of four points. Thecalculated deformation gradient tensor is calculated for the virtualcenter of gravity S. FIG. 21 schematically illustrates a four-sidedfacet.

This model of calculation assumes that the pure rigid body displacement,which the individual line elements received in addition to theirdeformation, cannot be modeled by the deformation gradient tensor F aswell. This means that for the calculation of the deformation gradienttensor F all points of a neighborhood may undergo a translation. Thistranslation may be different for the undeformed and the deformed state.The translation is chosen such that the point for which the deformationgradient tensor is being calculated is shifted into the origin.

A.4 Calculation of the Deformation Gradient Tensor from a 3DDisplacement Field

The description so far dealt in detail with the calculation of strain in2D. However, the measuring data consist of three-dimensional Cartesiancoordinates of the specimen's surface. In order to be able to use theabove models of calculation, the 3D data has to be transformed into the2D space.

A.4.1 The Tangential Model

The first model assumes that the local neighborhood of a point can bewell approximated by a tangential plane. Due to the arbitrarydeformation of the surface, the tangential plane needs to be calculatedseparately for the deformed and undeformed state. The points in thelocal neighborhood are then projected perpendicularly onto thetangential plane. The result is two sets of points, for the deformed andundeformed state, in the two-dimensional space in which the strain nowcan be calculated. Summarized, this process consists of the followingtasks:

-   -   Calculation of the tangential plane    -   Transformation of the 3D neighborhoods into the tangential        planes    -   Coordinate transformation of the tangential plane into the 2D        space    -   Calculation of the deformation gradient tensor from the 2D sets        of points

A.4.2 The Spline Model

The tangential model described above provides good results as long asthe assumption of the linearization of a local neighborhood of points isvalid. In deep drawing, the deformed materials are mostly continuouslycurved planes. The problem then is to apply the characteristics to bemeasured to the respective object in such a frequency that theassumption of local linearity is still given. However, thischaracteristic can hardly be provided in reality. Therefore, it isbetter to use other models which are more accurate in modeling the trueshape of the surface. Splines are a good model for continuously curvedlines.

In order to calculate the side length not only according to a linearmodel, it is necessary to have more information than two points on aside. This means that the adjacent points of a four-sided facet have tobe included in the calculations. FIG. 22 shows the adjacent points ofthe cross-hatched four-sided facet.

In the facet, the side lengths are calculated using the formed splines.The resulting lengths can be used to construct a quadrangle in thetwo-dimensional space. Then the strain calculations described above canbe used.

A.5 Bibliography for Strain Theory

1) Aramis User Manual v5.4.1 (GOM mbH) at pp. 129-135.2) Hibbitt, Karlsson and Lorensen, Inc. ABAQUS—Theory Manual, 5.7 ed.

3) Becker und Burger. Kontinuumsmechanik. [“Continuum Mechanics]Teubner-Verlag, 1975.

4) Malvern. Introduction to the Mechanics of a Continuous Medium.Prentice-Hall, 1969.5) Hahn. Elastizitatstheorie. Teubner-Verlag, 1984.6) Kopp und Wiegels. Einfuhrung in die Umformtechnik. [“Introduction toTransformation Technique”] Verlag der Augustinus Buchhandlung, 1998.The following reference numbers listed below are used in thespecification:

Ref. No. Meaning L Length H Height W Width α camera angle (alpha)  1operational block  2 operational block  3 operational block  4operational block  5 operational block  6 operational block  10 Camera,left  11 Camera lens, left  12 Camera rotation axis  13 camera adapterplate  15 camera support  16 tripod  18 computer  20 Camera, right  21Camera lens, right  24 angle bisector by laser pointer  25 base distance 28 laser pointer  30 measuring distance  34 center of measuring volume 35 specimen to measure  40 face of person  45 pattern  50 pixel  52Linitial facet, left camera  52R initial facet, right camera  54Ldeformed facet, left camera  54R deformed facet, right camera  60midstroke region  70 small dot  71 intermediate dot  72 large dot  73transfer paper  75 imaginary nose-ear line  76 imaginary lip line  77blade unit  77′ displaced blade unit  80 measurement area  81measurement area  82 measurement area  90 blunt probe 100 strain band101 strain band 102 strain band 103 strain band 104 strain band 105strain band 106 strain band

The dimensions and values disclosed herein are not to be understood asbeing strictly limited to the exact numerical values recited. Instead,unless otherwise specified, each such dimension is intended to mean boththe recited value and a functionally equivalent range surrounding thatvalue. For example, a dimension disclosed as “40 mm” is intended to mean“about 40 mm.”

All documents cited in the Detailed Description of the Invention are, inrelevant part, incorporated herein by reference; the citation of anydocument is not to be construed as an admission that it is prior artwith respect to the present invention. To the extent that any meaning ordefinition of a term in this document conflicts with any meaning ordefinition of the same term in a document incorporated by reference, themeaning or definition assigned to that term in this document shallgovern.

While particular embodiments of the present invention have beenillustrated and described, it would be obvious to those skilled in theart that various other changes and modifications can be made withoutdeparting from the spirit and scope of the invention. It is thereforeintended to cover in the appended claims all such changes andmodifications that are within the scope of this invention.

1. A removable tattoo for patterning a section of skin to provide a reference marking for use in optical skin deformation measurements, comprising a substrate (73), and a pattern (45) comprising a plurality of indicia randomly distributed to form a pattern density of between about 40% and about 60%.
 2. The removable tattoo of claim 1, wherein the indicia comprises dots.
 3. The removable tattoo of claim 2, wherein the dots comprise two or more different sized dots (70, 71).
 4. The removable tattoo of claim 2, wherein the dots comprise three different sized dots (70, 71, 72).
 5. The removable tattoo of claim 1, wherein the pattern density is about 50%.
 6. The removable tattoo of claim 1, wherein the pattern density is about 42.5%.
 7. The removable tattoo of claim 1, wherein the indicia is transferable to the skin by wetting with an alcohol.
 8. The removable tattoo of claim 1, wherein the substrate (73) is a paper.
 9. The removable tattoo of claim 8, wherein the paper is chosen from a group of paper consisting of blotting paper and cigarette paper.
 10. The removable tattoo of claim 1, wherein the indicia comprises a substantially water-insoluble ink or dye.
 11. The removable tattoo of claim 10, wherein the indicia comprises an oil-based ink or dye.
 12. The removable tattoo of claim 1, wherein the indicia is devoid of a cover layer formed above said indicia opposite said substrate (73).
 13. The removable tattoo of claim 1 being devoid of an adhesive layer atop said indicia.
 14. A moisture-activated, removable tattoo for patterning a section of skin to provide a reference marking for use in optical-based skin deformation measurements, comprising a substrate (73), and a random pattern (45) comprising a plurality of distributed dots, said dots comprising an ink or dye, said ink or dye being substantially water insoluble and being substantially soluble in an alcohol.
 15. The removable tattoo of claim 14, wherein the dots comprise two or more different sized dots (70, 71).
 16. The removable tattoo of claim 14, wherein the dots comprise three different sized dots (70, 71, 72).
 17. The removable tattoo of claim 14, wherein the random pattern (45) has a pattern density of between about 40% and about 60%.
 18. The removable tattoo of claim 17, wherein the pattern density is about 50%.
 19. The removable tattoo of claim 17, wherein the pattern density is about 42.5%.
 20. The removable tattoo of claim 14, wherein the substrate (73) is a paper.
 21. The removable tattoo of claim 20, wherein the paper is chosen from a group of paper consisting of blotting paper and cigarette paper.
 22. The removable tattoo of claim 14, wherein the dots comprise an oil-based ink or dye.
 23. The removable tattoo of claim 14, wherein the ink or dye comprises a pigment.
 24. The removable tattoo of claim 14, wherein the substrate (73) is moisture permeable.
 25. The removable tattoo of claim 1, wherein the dots are devoid of a cover layer formed above said dots opposite said substrate (73).
 26. The removable tattoo of claim 14 being devoid of an adhesive layer atop said dots. 